Stochastic Models in Geosystems

1. Front Matter

   Pages i-x

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2. Seismic Coda Waves: A Stochastic Process in Earth’s Lithosphere

   • Keiiti Aki

   Pages 1-24

3. One Dimensional Random Walk in a Random Medium

   • R. F. Anderson, S. A. Molchanov

   Pages 25-56

4. Cascade of Scaling Gyroscopes: Lie Structure, Universal Multifractals and Self-Organized Criticality in Turbulence

   • Y. Chigirinskaya, D. Schertzer

   Pages 57-81

5. A Non-Linear Model for Fluid Parcel Motions in the Presence of Many Large and Meso-Scale Vortices

   • L. Ju. Fradkin, A. R. Osborne

   Pages 83-96

6. Scale-Dependent Ocean Wave Turbulence

   • Roman E. Glazman

   Pages 97-114

7. A Survey of Cascades with Applications from Geosciences

   • Vijay K. Gupta, Ed Waymire

   Pages 115-127

8. The Role of Statistical Models in Turbulence Theory

   • J. R. Herring

   Pages 129-136

9. Ocean Circulation: Flow in Probability under Statistical Dynamical Forcing

   • Greg Holloway

   Pages 137-148

10. Random Topography in Geophysical Models

    • V. Klyatskin, D. Gurarie

    Pages 149-169

11. Dynamical and Statistical Characteristics of Geophysical Fields and Waves and Related Boundary-Value Problems

    • V. I. Klyatskin, W. A. Woyczynski

    Pages 171-208

12. Localization of Low Frequency Elastic Waves

    • W. Kohler, G. Papanicolaou, B. White

    Pages 209-217

13. Stochastic Forcing of Oceanic Motions

    • Peter Müller

    Pages 219-237

14. Radiative Transfer in Multifractal Atmospheres: Fractional Integration, Multifractal Phase Transitions and Inversion Problems

    • Catherine Naud, Daniel Schertzer, Shaun Lovejoy

    Pages 239-267

15. The Morphology and Texture of Anisotropic Multifractals Using Generalized Scale Invariance

    • S. Pecknold, S. Lovejoy, D. Schertzer

    Pages 269-311

16. Short-Correlation Approximation in Models of Turbulent Diffusion

    • L. Piterbarg

    Pages 313-352

17. Comments on Estimation and Prediction for Autoregressive and Moving Average Nongaussian Sequences

    • Murray Rosenblatt

    Pages 353-358

18. Probability Distributions of Passive Tracers in Randomly Moving Media

    • A. I. Saichev, W. A. Woyczynski

    Pages 359-399

19. Three-Dimensional Burgers’ Equation as a Model for the Large-Scale Structure Formation in the Universe

    • Sergei F. Shandarin

    Pages 401-413

20. Non-Mean Field Approach to Self-Organization of Landforms Via Stochastic Merger

    • Hubert Shen

    Pages 415-425

This IMA Volume in Mathematics and its Applications STOCHASTIC MODELS IN GEOSYSTEMS is based on the proceedings of a workshop with the same title and was an integral part of the 1993-94 IMA program on "Emerging Applications of Probability." We would like to thank Stanislav A. Molchanov and Wojbor A. Woyczynski for their hard work in organizing this meeting and in edit­ ing the proceedings. We also take this opportunity to thank the National Science Foundation, the Office of N aval Research, the Army Research Of­ fice, and the National Security Agency, whose financial support made this workshop possible. A vner Friedman Willard Miller, Jr. v PREFACE A workshop on Stochastic Models in Geosystems was held during the week of May 16, 1994 at the Institute for Mathematics and Its Applica­ tions at the University of Minnesota. It was part of the Special Year on Emerging Applications of Prob ability program put together by an organiz­ ing committee chaired by J. Michael Steele. The invited speakers represented a broad interdisciplinary spectrum including mathematics, statistics, physics, geophysics, astrophysics, atmo­ spheric physics, fluid mechanics, seismology, and oceanography. The com­ mon underlying theme was stochastic modeling of geophysical phenomena and papers appearing in this volume reflect a number of research directions that are currently pursued in these areas.

• astrophysics
• dynamical systems
• geophysics
• mechanics
• statistics

• Department of Mathematics, University of North Carolina at Charlotte, Charlotte, USA

  Stanislav A. Molchanov

• Center for Stochastic and Chaotic Processes in Science and Technology, Case Western Reserve University, Cleveland, USA

  Wojbor A. Woyczynski

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